Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 10 - Compositions, Inverses, and Combinations of Functions - 10.3 Combinations of Functions - Exercises and Problems for Section 10.3 - Exercises and Problems - Page 421: 26

Answer

$\dfrac{x^2+3x+1}{x+1}$

Work Step by Step

We perform the given operation and then combine like terms as necessary in order to simplify. $f(\dfrac{1}{x})+\dfrac{1}{f(x)}=\dfrac{1}{\dfrac{1}{x}+1}+\dfrac{1}{1/x+1}\\=\dfrac{x+(x+1)(1+x)}{1+x}\\=\dfrac{x+x^2+2x+1}{1+x}\\=\dfrac{x^2+3x+1}{x+1}$
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